Problem: What do the following two equations represent? $-4x-5y = 1$ $4x+5y = 2$
Solution: Putting the first equation in $y = mx + b$ form gives: $-4x-5y = 1$ $-5y = 4x+1$ $y = -\dfrac{4}{5}x - \dfrac{1}{5}$ Putting the second equation in $y = mx + b$ form gives: $4x+5y = 2$ $5y = -4x+2$ $y = -\dfrac{4}{5}x + \dfrac{2}{5}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.